June 1995
Intermediate to advanced
438 pages
10h 53m
English
Content preview from Graphics Gems V (IBM Version)
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IV.3
Circular Arc Subdivision
Turkowski Ken, Apple Computer, Inc. Cupertino, California. E-mail address: turk@apple.com
Introduction
This gem presents an algebraic solution to the rendering problem of circular arcs. These forms commonly arise in graphic design. For instance, well-designed typefaces may apply a very slight curvature on a portion of a letterform to produce a profound aesthetic effect. 1
A circular arc may be represented in terms of the center and radius of its parent circle, plus the starting and ending angles θst and θend. This suggests a first-principles solution that generates successive points on the arc by evaluating the sine and cosine of a series of intermediate angles:
Clearly, this approach is computationally ...
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